Let $A=\left\{n\in N\mid n^2\le n+10,000\right\}, B=\left\{3k+1\mid k\in N\right\}$ and $C=\left\{2k\mid k\in N\right\},$ then the sum of all the elements of the set $A\cap \left(B-C\right)$ is equal to ________.

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

Let $S_1, S_2$ and $S_3$ be three sets defined as

$S_1=\{z\in ℂ:|z-1|\le \sqrt{2}\},$

$S_2=\{z\in ℂ:Re((1-i)z)\ge 1\}$ and

$S_3=\{z\in ℂ:Im(z)\le 1\}.$

Then, the set $S_1\cap S_2\cap S_3$

Define a relation $R$ over a class of $n\times n$ real matrices $A$ and $B$ as "$ARB$ iff there exists a non-singular matrix $P$ such that $PA{P}^{-1}=B$". Then which of the following is true ?